Computing Network Reliability in Time Polynomial in the Number of Cuts

We present a new algorithm that computes the probability that there is an operating path from a node s to a node t in a stochastic network. The computation time of this algorithm is bounded by a polynomial in the number of (s, t)-cuts in the network. We also examine the complexity of other connectedness reliability problems with respect to the number of cutsets and pathsets in the network. These problems are distinguished as either having algorithms that are polynomial in the number of such sets, or having no such algorithms unless P = NP.